Einstein-Podolsky-Rosen correlations in second-harmonic generation

A quantum model for singly resonant second-harmonic generation in a cavity with transverse degrees of freedom is analyzed. An instability threshold for pattern formation exists in this system. Below threshold, a strong modulation of the noise is demonstrated in the transverse structure of the far field. The performed analysis encompasses both one- and two-point correlation functions. The noise in a single far-field point is generally above the classical vacuum noise level. In contrast, strong nonclassical two-point correlations are encountered between opposite emission directions in the far field. For the fundamental field the correlations are shown to be of the Einstein-Podolsky-Rosen type, thus establishing a remarkable analog to the quantum correlations found in a nondegenerate optical parametric oscillator.